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# Points B and C lie on AD. The length of AB is 4 times the length of BD

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Math Expert
Joined: 02 Sep 2009
Posts: 58428
Points B and C lie on AD. The length of AB is 4 times the length of BD  [#permalink]

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27 Mar 2019, 21:00
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Difficulty:

25% (medium)

Question Stats:

75% (02:30) correct 25% (03:29) wrong based on 32 sessions

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Points B and C lie on AD. The length of AB is 4 times the length of BD, and the length of AC is 9 times the length of CD. The length of BC is what fraction of the length of AD ?

(A) 1/36
(B) 1/13
(C) 1/10
(D) 5/36
(E) 1/5

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Intern
Joined: 27 Sep 2018
Posts: 37
Re: Points B and C lie on AD. The length of AB is 4 times the length of BD  [#permalink]

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27 Mar 2019, 22:08
AB=4BD

Also AC=9CD
MULTIPLYING (I) BY 2 AND SUBTRACTING BY (II)

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Intern
Joined: 28 Aug 2018
Posts: 12
Re: Points B and C lie on AD. The length of AB is 4 times the length of BD  [#permalink]

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27 Mar 2019, 22:34
AB = 4BD = 4(BC+BD) = 4BC + 4CD.

=> AB = 4BC + 4CD
Adding BC to both sides of the equality, AB + BC = 5BC + 4CD
=> AC = 5BC + 4CD

We already know, AC = 9CD. Therefore, 9CD = 5BC + 4CD => 5CD = 5BC => CD = BC.
Hence, AC = 9BC.

Ans. option C.
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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9701
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Re: Points B and C lie on AD. The length of AB is 4 times the length of BD  [#permalink]

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27 Mar 2019, 23:11
1
Bunuel wrote:
Points B and C lie on AD. The length of AB is 4 times the length of BD, and the length of AC is 9 times the length of CD. The length of BC is what fraction of the length of AD ?

(A) 1/36
(B) 1/13
(C) 1/10
(D) 5/36
(E) 1/5

A-------------------------------------------------D

A----------------------------------B--------------D
AB = 8, BD = 2 (Ratio of 4:1)

A-------------------------------------------C-----D
AC = 9, CD = 1 (Ratio of 9:1)

BC = AC - AB = 9 - 8 = 1

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Karishma
Veritas Prep GMAT Instructor

Re: Points B and C lie on AD. The length of AB is 4 times the length of BD   [#permalink] 27 Mar 2019, 23:11
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